Epidemiology generates a major part of the scientific knowledge needed for programs in cancer prevention and regulation of carcinogenic exposures. Case-control and cohort studies serve not only to identify carcinogenic risk factors but also to investigate dose-time-response relationships for purposes of quantitative risk assessment and the planning of intervention strategies. Statistical concepts are crucial for understanding the logical foundations of such studies and for devising appropriate methods of study design and data analysis. The broad objective of this proposal is to create new and efficient statistical methods or design and analysis of epidemiologic studies that are well suited to the quantification of human cancer risk, and to make the new tools available in a form suitable for immediate application by medical epidemiologists and others without extensive technical background. One specific goal is to generate families of statistical models for relative and absolute risk that are flexible enough to encompass competing hypotheses about the nature of the carcinogenic process. By comparing the goodness-of-fit of different models within each class, and by examining the stability of the fitted model to perturbations in the underlying data, it will be possible to evaluate the extent to which the data support one hypothesis over another. Use of general population cancer rates in the model should improve the efficiency of the analysis and the amount of information that is extracted from the data. Design modifications are suggested that should facilitate efficient estimation of relative risks with fewer subjects and lower costs. Mathematical analysis will be used to generate the new statistical models and investigate their theoretical properties. The methods will be tested immediately on several important sets of cancer epidemiology data. Their numerical characteristics will be investigated by Monte Carlo studies using parameter settings determined from these real applications. The new methodology will be implemented on microcomputers and described in revisions of established textbooks so as to facilitate its transmission to research workers.